Implied volatility is a quantity related to the price of a traded financial option to buy (“call” option) or to sell (“put” option) a particular asset. Specifically, implied volatility represents the market's estimate of the future price volatility of the underlying asset. According to results of Black and Scholes, the market price of an option depends solely on the asset's future price volatility, the current price of the underlying asset, the risk-free interest rate, the dividend yield (if any) from the underlying asset, the exercise price of the option, and the time to expiration.
In the case of “European” options (options which can only be exercised at expiration), Black and Scholes present a formula for the calculation of the fair market price of the option given its volatility and other inputs. Subsequent researchers showed how this formula could be inverted, essentially solving for the volatility using the other inputs and the current market price of the option. This value is referred to as implied volatility, and is used by options traders as an indication of the relative value of an option, in much the same way that yield serves as a measure of the relative value of a bond. An equivalent Black-Scholes type formula does not exist for American options.
Option pricing and implied volatility are known in the art, and further discussion of them provided in the following publications, all of which are fully incorporated herein by reference: Black, F. and M. Scholes, 1973, “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, 81, 637-654; Cox, J. C., S. A. Ross, and M. Rubinstein, 1979, “Option Pricing: A Simplified Approach”, Journal of Financial Economics, 7, 229-263; Cox, J. C., and M. Rubinstein, 1985, “Options Markets”, Prentice-Hall, Englewood Cliffs, N.J.; and Latane, H., and R. Rendleman, Jr., 1976, “Standard Deviation of Stock Price Ratios Implied in Option Prices”, Journal of Finance, 31, 369-382.